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Reply Sat 26 Jul, 2008 05:49 pm
Can someone help me with this? I am to derive the conclusions of the following arguments, using any of the 19 rules:


1. (A & U) < > ~R
2. ~(~R v ~A) / ~U
3.--R & --A ( 2) De M
4.R & A (3) DN
5.R (4) Simp.

And I am stuck from here... can't get to -U

And the second one:
[INDENT]1. (B > G) & (F > N)
2. ~(G & N) / ~(B & F) [/INDENT]
 
Zetetic11235
 
Reply Sat 26 Jul, 2008 07:30 pm
@cooper phil,
cooper wrote:
Can someone help me with this? I am to derive the conclusions of the following arguments, using any of the 19 rules:


1. (A & U) < > ~R
2. ~(~R v ~A) / ~U
3.--R & --A ( 2) De M
4.R & A (3) DN
5.R (4) Simp.

And I am stuck from here... can't get to -U


So you need the conclusion -U right?
Well, it seems like looking at 1 and 5 gives ~U: ~(A&U) (1,5 i think thats by M.T.) thus (~Av~U) by De M. But A is true by (4) so you have a false proposition with another one, thus the other is true by disjunctive syllogism thus ~U.
cooper wrote:

And the second one:
[INDENT]1. (B > G) & (F > N)
2. ~(G & N) / ~(B & F)
[/INDENT]

Ill leave this one up to you, I hope the above helps by example.
 
cooper phil
 
Reply Sat 26 Jul, 2008 07:45 pm
@Zetetic11235,
Thanks.I don't think 1 and 5 can get (-Av-U) using MT...the sign is < >, not >...
 
Zetetic11235
 
Reply Sat 26 Jul, 2008 09:17 pm
@cooper phil,
Keep in mind that since 1 is true, it is an equivalence relation between A&U and ~R. Equivalence is an iff statement that is a tautology. I'm not sure what rule you would use, but its obviously true by truth table.
 
VideCorSpoon
 
Reply Sat 26 Jul, 2008 11:33 pm
@Zetetic11235,
These are pretty tough. The first one took a little time to do. Also, thanks Zentetic for your extrapolations in post #2, ~(A&U) was right on the money when the proof was reversed. Good eye.
http://i38.tinypic.com/swxvy8.jpg
The second one is a tough one. I think it may require an indirect or conditional proof. I started the deconstruction if anyone wants to hash it out in the mean time.
http://i36.tinypic.com/260fp7a.jpg
 
VideCorSpoon
 
Reply Sun 27 Jul, 2008 08:57 am
@VideCorSpoon,
http://i34.tinypic.com/14klie0.jpg
If you have any questions, let us know.

Also, Welcome to the forum!
 
 

 
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